It is generally a terrible idea to build a building from the plans of a dead architect, and it happens more often than you would think. Frank Lloyd Wright’s Yahara boathouse, designed in 1905 for a site in Madison, Wisconsin, and never built, finally went up a few years ago—in Buffalo. In 2005 a house Wright had begun to design in 1950 for a waterfront site in upstate New York was resurrected by a new owner of the property, who was determined to build it despite the fact that Wright had never finished the design and no complete set of drawings for it even existed.

But even when an architect figured out a project to the last detail and a future client wants to be faithful to his ideas, there are other problems. Architects often tend to rethink elements at the last minute, as buildings are going up and new ideas come to mind. If the architect is no longer around, there is no way to account for what he or she might have been moved to do differently. These spontaneous changes can be miniscule but critical, and without them, a design may feel dutiful but eerily flat.

Posthumous architecture tends also to ignore the fact that the world has inevitably changed since a project was first designed. The church of Saint-Pierre in Firminy, France, designed by Le Corbusier, wasn’t started until six years after his death, in 1965, and wasn’t finished until 2006, with numerous changes from the architect’s original plans. Who is to say whether Le Corbusier would have designed the same building had he actually been alive in the 1970s? Antonio Gaudi’s extraordinary Sagrada Familia cathedral in Barcelona, unfinished at the time of the architect’s death in 1926, is continuing to go ahead today, in a misguided homage to Gaudi’s memory that is especially foolhardy, since Gaudi tended to improvise many of the details of his architecture as it was going up, and he left only some general drawings for the whole cathedral, meaning that a lot of what is going up now in Barcelona is guesswork. You could say it’s an effort to channel the architect’s spirit, which is generally not the soundest way to go about making a building.

So it’s something of a miracle that New York City’s Franklin Delano Roosevelt Memorial by Louis Kahn, a piece of posthumous architecture that has just opened at the southern tip of Roosevelt Island, in the East River, is so absolutely right. It is the first time a work of posthumous architecture has made me feel elated, not offended, and left me absolutely certain that the right thing had been done. The memorial was designed in 1974, shortly before Kahn’s sudden death of a heart attack in Pennsylvania Station. He was, at that point, the most revered living architect in the United States, a kind of philosopher-king of his profession whose oeuvre was small, and consisted almost entirely of masterworks such as the Salk Center in La Jolla, California, the Kimbell Art Museum in Forth Worth, and the Yale Center for British Art in New Haven.

Kahn in his lifetime never managed to build anything in New York, and for several decades after his death it seemed certain that this project would die with him. It was conceived in 1973, just as Welfare Island was being rechristened Roosevelt Island and becoming the site of an ambitious redevelopment project; the memorial, it was hoped, would be the symbol that would remind everyone just why the place had been named Roosevelt Island. The architect’s death coincided with the New York City fiscal crisis of the 1970s, and the fact that, suddenly, there was not only no architect but also no money seemed to doom the project. The new town on Roosevelt Island grew just fine without it, and in time most people seemed to forget that Kahn’s plan had ever existed.

William vanden Heuvel, a passionate admirer of Roosevelt who was an assistant to Robert Kennedy when Kennedy was attorney general and later served as an American diplomat, did not forget. In 2005, vanden Heuvel decided to try to resurrect the memorial. He managed to raise $53 million from private sources, and to convince the city and the state that the project should go ahead.

Vanden Heuvel’s determination—and that of Gina Pollara, an architect who headed the building effort—made the project happen, but it doesn’t explain why the memorial is as good as it is, and why it has been spared the lifeless quality of so many posthumous buildings. One thing that helped is that Kahn left fairly complete drawings and had made almost every aesthetic decision, so while the project posed some significant engineering challenges for Weidlinger, its structural engineers, the architectural firm that was given charge of overseeing construction, Mitchell/Giurgola, did not have major design decisions to make. And Kahn, working with his longtime landscape architect Harriet Pattison, had been clear about how he wanted the long rows of trees to look. It was up to the contemporary landscape architects, Villa/Sherr, to try to find the 125 trees that would meet his specifications.

But it is really the simple, abstract, and powerful nature of Kahn’s architecture that allowed this to be built so convincingly nearly 40 years after it was designed. I don’t want to use the word “timeless,” because nothing is truly timeless, and Kahn’s architecture was very much of the 20th century. But even as his work marks its time, it has always seemed to transcend its time, almost to transcend time itself; it is stark, but in an almost primal way. Kahn designed buildings that were modern and at the same time looked as if they had been there forever. He went back to the very basics of architecture, to its underlying truths, and he expressed them as no other architect could. With Kahn you feel solids and voids and masses and light and shadow. Build it in 1974, build it in 2012—when it is Louis Kahn it doesn’t seem quite to matter as much as it would with some other architect’s work.

The F.D.R. memorial has a design that seems simple, but is in fact quite complex and subtle. You approach it from the north, and you first see a monumental staircase, a hundred feet wide, that leads up to a long, tapering lawn flanked by twin rows of linden trees. (There are also walkways on either side of the staircase, beside the water, that bypass the stairs.) The lawn slopes gradually downward as it narrows toward a central focal point: a granite piazza containing an enlarged version of the famous bust of Roosevelt by the sculptor Jo Davidson, set within a granite alcove. Behind the sculpture is what Kahn called “the room”—a three-sided room of granite, its fourth side open to the water, its roof open to the sky.

An excerpt from Roosevelt’s famous “Four Freedoms” speech—in which, on the eve of World War II, he spoke of freedom of speech, freedom of worship, freedom from want, and freedom from fear as fundamental human rights—is carved on the back of the enclosure containing the sculpture. There are no other words, nor should there be. The walls of Kahn’s room are of immense, six-foot deep blocks of granite, set one inch apart. Here, as you look out to the city—and to the United Nations, which could not be more appropriate—you feel the metaphorical power of architecture: openness to the world is balanced with stability, protection, solidity. You have a sense of looking both inward and outward; this space feels at once as contemplative as a chapel, and as connected to the world as Times Square.

The huge slabs of granite are flame-finished, but the inside surfaces facing the one-inch gaps between the slabs are polished, a brilliant detail. You get tiny glimpses of the water and the skyline as you peer through, and the polish enhances the light. At the corners, where three blocks of granite meet, there is another detail that only Kahn could have conceived: you look directly into the corner of the corner piece, which appears to float within the inch-wide gaps on either side. Maybe all of this, too, is metaphor, the great blocks of granite an inch apart telling us that, even though we are not directly connected, if we stand together we can make something solid. The corner detail is also a reminder that, often, the greatest and most beautiful things are barely visible.

The sky feels big here, bigger than anywhere else in New York. There is nothing high to interfere with the great dome of sky, and so you feel, paradoxically, closer to nature here than even in Central Park. The sky is as much a part of Kahn’s design as the river, and the skyline. This is a memorial but it is also a park, a park that shows, as well as any place, Kahn’s genius. It narrows to a laser-like focus on Roosevelt, and then it opens up to connect you to the world.

Below, more buildings completed for star architects after their deaths.